過去の記録

過去の記録 ~08/18本日 08/19 | 今後の予定 08/20~

トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Dylan Thurston 氏 (Columbia University)
Combinatorial Heegaard Floer homology (ENGLISH)
[ 講演概要 ]
Heegaard Floer homology is a powerful invariant of 3- and 4-manifolds.
In 4 dimensions, Heegaard Floer homology (together with the
Seiberg-Witten and Donaldson equations, which are conjecturally
equivalent), provides essentially the only technique for
distinguishing smooth 4-manifolds. In 3 dimensions, it provides much
geometric information, like the simplest representatives of a given
homology class.

In this talk we will focus on recent progress in making Heegaard Floer
homology more computable, including a complete algorithm for computing
it for knots.

2012年04月23日(月)

代数幾何学セミナー

17:10-18:40   数理科学研究科棟(駒場) 122号室
いつもと時間が違います。
安田 健彦 氏 (大阪大学)
Motivic integration and wild group actions (JAPANESE)
[ 講演概要 ]
The cohomological McKay correspondence proved by Batyrev is the equality of an orbifold invariant
and a stringy invariant. The former is an invariant of a smooth variety with a finite group action and the latter is
an invariant of its quotient variety. Denef and Loeser gave an alternative proof of it which uses the motivic integration theory developped by themselves.
Then I pushed forward with their study by generalizing the motivic integration to
Deligne-Mumford stacks and reformulating the cohomological McKay correspondence from the viewpoint of
the birational geometry of stacks.
However all of these are about tame group actions (the order of a group is not divisible by the characteristic of the base field),
and the wild (= not tame) case has remained unexplored.
In this talk, I will explain my attempt to examine the simplest situation of the wild case. Namely linear actions of a cyclic group
of order equal to the characteristic of the base field are treated. A remarkable new phenomenon is that the space of generalized
arcs is a fibration over an infinite dimensional space with infinite dimensional fibers, where the base space is the space of
Artin-Schreier extensions of $k((t))$, the field of Laurent series.

2012年04月21日(土)

調和解析駒場セミナー

13:30-17:00   数理科学研究科棟(駒場) 122号室
寺澤祐高 氏 (東大数理) 13:30-15:00
Dyadic, classical and martingale harmonic analysis (JAPANESE)
[ 講演概要 ]
筒井容平 氏 (早稲田大学) 15:30-17:00
A_\\\\infty constants between BMO and weighted BMO (JAPANESE)
[ 講演概要 ]

2012年04月20日(金)

統計数学セミナー

14:50-16:00   数理科学研究科棟(駒場) 006号室
参加をご希望される方は鎌谷 (阪大基礎工); kamatani at sigmath.es.osaka-u.ac.jpまでご連絡ください.
小池 祐太 氏 (東京大学大学院数理科学研究科)
非同期従属サンプリング下でのpre-averaged Hayashi-Yoshida estimatorの漸近混合正規性について (JAPANESE)
[ 講演概要 ]
2つのセミマルチンゲールの離散観測データからそれらの累積 コボラティリティ, すなわち第2特性量を推定する問題は, 金融分野の高頻度デ ータ解析への応用を目的として近年盛んに研究されている. 最近の研究では, 次 の4つの問題:(1)サンプリングの非同期性,(2)サンプリングの観測過程への従属 性,(3)マイクロストラクチャーノイズ,(4)ジャンプ, を処理する方法の研究が主 流となっている. 本発表では, (1)と(3)を処理するために提案されたpre- averaged Hayashi-Yoshida estimatorを少し修正して, (1)-(3)のもとでこの推 定量が一致性および漸近混合正規性をもち, かつ最適収束レートを達成すること を示す.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/01.html

2012年04月18日(水)

代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 056号室
Alan Lauder 氏 (University of Oxford)
Explicit constructions of rational points on elliptic curves (ENGLISH)
[ 講演概要 ]
I will present an algorithm for computing certain special
values of p-adic L-functions, and discuss an application to
the efficient construction of rational points on elliptic curves.

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
嶌田洸一 氏 (東大数理)
Classification of Group Actions on Factors (after Masuda) (JAPANESE)

2012年04月17日(火)

トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Eriko Hironaka 氏 (Florida State University)
Pseudo-Anosov mapping classes with small dilatation (ENGLISH)
[ 講演概要 ]
A mapping class is a homeomorphism of an oriented surface
to itself modulo isotopy. It is pseudo-Anosov if the lengths of essential
simple closed curves under iterations of the map have exponential growth
rate. The growth rate, an algebraic integer of degree bounded with
respect to the topology of the surface, is called the dilatation of the
mapping class. In this talk we will discuss the minimization problem
for dilatations of pseudo-Anosov mapping classes, and give two general
constructions of pseudo-Anosov mapping classes with small dilatation.

2012年04月16日(月)

代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室
三浦 真人 氏 (東大数理)
Toric degenerations of minuscule Schubert varieties and mirror symmetry (JAPANESE)
[ 講演概要 ]
Minuscule Schubert varieties admit the flat degenerations to projective
Hibi toric varieties, whose combinatorial structure is explicitly
described by finite posets. In this talk, I will explain these toric
degenerations and discuss the mirror symmetry for complete intersection
Calabi-Yau varieties in Gorenstein minuscule Schubert varieties.

複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 126号室
奥山裕介 氏 (京都工芸繊維大学)
Fekete configuration, quantitative equidistribution and wanderting critical orbits in non-archimedean dynamics
(JAPANESE)

2012年04月14日(土)

保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 123号室
刈山和俊 氏 (尾道市立大学経済情報学部
) 13:30-14:30
GL_m(D)の離散系列表現の形式次数に関する明示公式 (JAPANESE)
宗野恵樹 氏 (東京大学数理科学研究科) 15:00-16:00
Moments of the derivatives of the Riemann zeta function (JAPANESE)
[ 講演概要 ]
In my talk, we consider the integral moments of the derivatives of the Riemann zeta function on the critical line. We give certain lower bounds for these moments under the assumption of the Riemann hypothesis.

2012年04月13日(金)

統計数学セミナー

14:50-16:00   数理科学研究科棟(駒場) 006号室
参加をご希望される方は鎌谷 (阪大基礎工); kamatani at sigmath.es.osaka-u.ac.jpまでご連絡ください.
鎌谷 研吾 氏 (大阪大学基礎工学研究科)
Asymptotic properties of MCMC for cumulative link model (JAPANESE)
[ 講演概要 ]
ベイズ統計学におけるCumulative link modelに対するマルコフ連鎖モンテカルロ法の 振る舞いを解析する. 前半では,一般的に使われている Albert and Chib (JASA 1993)による手法は局所退化性を持ち, 極めて悪い収束レートを持つことを示す.また改善手法と一般に みなされている手法(Marginal augmentation; MA, Liu and Wu 1999, Meng and Dyk 1999)も, ある射影を施すことでやはり局所退化していることを示す. 後半は,MAを若干変更することで,カテゴリの数があまり多くなければ, 殆ど計算負荷を変えること無く局所一致性を持つ手法を構成できる(MA2)事を示す. またカテゴリの数によらず常に局所一致性を持つ手法(MMA)も紹介する. 数値実験を通してこれらの振る舞いを比較する. 前半部分は一部,昨年の駒場のSART2011での講演と同じである.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/00.html

2012年04月11日(水)

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Shweta Sharma 氏 (Univ. Paris Sud)
Mathematical Aspects of Fractional Quantum Hall Effect (ENGLISH)

代数学コロキウム

17:30-18:30   数理科学研究科棟(駒場) 056号室
Damian Rossler 氏 (CNRS, Universite de Toulouse)
Around the Mordell-Lang conjecture in positive characteristic (ENGLISH)
[ 講演概要 ]
Let V be a subvariety of an abelian variety A over C and let G\\subseteq A(C) be a subgroup. The classical Mordell-Lang conjecture predicts that if V is of general type and G\\otimesQ is finite dimensional, then V\\cap G is not Zariski dense in V. This statement contains the Mordell conjecture as well as the Manin-Mumford conjecture (for curves). The positive characteristic analog of the Mordell-Lang conjecture makes sense, when A is supposed to have no subquotient, which is defined over a finite field. This positive characteristic analog was proven in 1996 by E. Hrushovski using model-theoretic methods. We shall discuss the prehistory and context of this proof. We shall also discuss the proof (due to the speaker) of the fact that in positive characteristic, the Manin-Mumford conjecture implies the Mordell-Lang conjecture (whereas this seems far from true in characteristic 0).

(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)

2012年04月10日(火)

トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
逆井 卓也 氏 (東京大学大学院数理科学研究科)
On homology of symplectic derivation Lie algebras of
the free associative algebra and the free Lie algebra (JAPANESE)
[ 講演概要 ]
We discuss homology of symplectic derivation Lie algebras of
the free associative algebra and the free Lie algebra
with particular stress on their abelianizations (degree 1 part).
Then, by using a theorem of Kontsevich,
we give some applications to rational cohomology of the moduli spaces of
Riemann surfaces and metric graphs.
This is a joint work with Shigeyuki Morita and Masaaki Suzuki.

2012年04月09日(月)

代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室
植田 一石 氏 (大阪大学)
On mirror symmetry for weighted Calabi-Yau hypersurfaces (JAPANESE)
[ 講演概要 ]
In the talk, I will discuss relation between homological mirror symmetry for weighted projective spaces, their Calabi-Yau hypersurfaces, and weighted homogeneous singularities.
If the time permits, I will also discuss an application to monodromy of hypergeometric functions.

複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 126号室
高山茂晴 氏 (東大数理)
Effective estimate on the number of deformation types of families of canonically polarized manifolds over curves
(JAPANESE)

2012年04月04日(水)

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
北海道大学のHPには、第1回(2004年9月29日)~第38回(2008年10月15日)までの情報が掲載されております。
Jens Hoppe 氏 (Sogang University / KTH Royal Institute of Technology)
Multi linear formulation of differential geometry and matrix regularizations (ENGLISH)
[ 講演概要 ]
We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for Weingarten's formula, the Ricci curvature and the Codazzi-Mainardi equations.
For matrix analogues of embedded surfaces we define discrete curvatures and Euler characteristics, and a non-commutative Gauss–Bonnet theorem is shown to follow. We derive simple expressions for the discrete Gauss curvature in terms of matrices representing the embedding coordinates, and a large class of explicit examples is provided.

2012年04月03日(火)

保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 123号室
刈山和俊 氏 (尾道市立大学経済情報学部
) 13:30-14:30
GL_m(D)の離散系列表現の形式次数に関する明示公式 (JAPANESE)
宗野恵樹 氏 (東京大学数理科学研究科) 15:00-16:00
Moments of the derivatives of the Riemann zeta function (JAPANESE)
[ 講演概要 ]
In my talk, we consider the integral moments of the derivatives of the Riemann zeta function on the critical line. We give certain lower bounds for these moments under the assumption of the Riemann hypothesis.

2012年03月23日(金)

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 117号室
Alex Kumjian 氏 (University of Nevada, Reno)
Higher Rank Graph $C^*$-algebras (ENGLISH)

講演会

10:30-11:30   数理科学研究科棟(駒場) 117号室
R. Penner 氏 (Aarhus/Caltech)
Cell decomposition of homotopy Deligne-Mumford. (ENGLISH)
[ 講演概要 ]
A long-standing problem has been to extend the ideal cell decomposition of Riemann's moduli space to its compactification by stable curves. In joint work with Doug LaFountain, we have solved this problem with an explicit generalization of fatgraphs. The solution immediately provides a construction of odd-degree cycles, which are conjectured to be non-trivial, thus addressing yet another long-standing issue.

2012年03月21日(水)

講演会

10:15-12:00   数理科学研究科棟(駒場) 123号室
R. Penner 氏 (Aarhus/Caltech)
Geochemical structure of biological macromolecules (ENGLISH)
[ 講演概要 ]
This first of two lectures will explain the basic combinatorial and geometrical structures of both protein and RNA. It is intended to set the stage of subsequent discussions for an audience with mathematical background.

講演会

15:15-17:00   数理科学研究科棟(駒場) 123号室
R. Penner 氏 (Aarhus/Caltech)
Moduli space techniques in computational biology
(ENGLISH)
[ 講演概要 ]
Basic fatgraph models of RNA and protein will be discussed, where edges are associated with base pairs in the former case and with hydrogen bonds between backbone atoms in the latter. For RNA, this leads to new methods described by context-free grammars of RNA folding prediction including certain classes of pseudo-knots. For protein, beyond these discrete invariants lie continuous ones which associate a rotation of
3-dimensional space to each hydrogen bond linking a pair of peptide units. Histograms of these rotations over the entire database of proteins exhibit a small number of "peptide unit legos" which can be used to advantage for the protein folding problem.

PDE実解析研究会

10:00-11:00   数理科学研究科棟(駒場) 056号室
北海道大学のHPには、第1回(2004年9月29日)~第38回(2008年10月15日)までの情報が掲載されております。
Chiun-Chang Lee 氏 (National Taiwan University)
The asymptotic behaviors of the solutions of Poisson-Boltzmann type of equations (ENGLISH)
[ 講演概要 ]
Understanding the existence of electrical double layers around particles in the colloidal dispersion (system) is a crucial phenomenon of the colloid science. The Poisson-Boltzmann (PB) equation is one of the most widely used models to describe the equilibrium phenomenon of an electrical double layer in colloidal systems. This motivates us to study the asymptotic behavior for the boundary layer of the solutions of the PB equation. In this talk, we introduce the precise asymptotic formulas for the slope of the boundary layers with the exact leading order term and the second-order term. In particular, these formulas show that the mean curvature of the boundary exactly appears in the second-order term. This part is my personal work.
On the other hand, to study how the ionic concentrations and ionic valences affect the difference between the boundary and interior potentials in an electrolyte solution, we also introduce a modified PB equation - New Poisson-Boltzmann (PB_n) equation - joint works with Prof. Tai-Chia Lin and Chun Liu and YunKyong Hyon. We give a specific formula showing the influence of these crucial physical quantities on the potential difference in an electrolyte solution. This cannot be found in the PB equation.

2012年03月16日(金)

談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 123号室
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00~16:30 (コモンルーム)。

柳 春(LIU, Chun) 氏 (東京大学大学院数理科学研究科/ペンシルバニア州立大学)
複雑流体について (ENGLISH)
[ 講演概要 ]
この講演では、タンパク質と生体液における粘弾性材料、液晶、イオン流体といった異方的複雑流体のエネルギー的な変分法手法の数学理論について取 り上げる。

混合液や溶液などの複雑流体は我々の日常生活にあふれている。これらの材料が示す複雑な現象や特性は、微視的相互作用と巨視的動力学の間の結合と 競合を反映している。我々はこれらのあらゆるマルチスケール・マルチフィジックスシステムに共通する基本的なエネルギー的変分構造を研究する。

この講演では、さまざまな複雑流体についてのモデリングに加えて、数学解析や数値計算まで触れたい。

2012年03月14日(水)

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
北海道大学のHPには、第1回(2004年9月29日)~第38回(2008年10月15日)までの情報が掲載されております。
Jürgen Saal 氏 (Technische Universität Darmstadt)
Exponential convergence to equilibria for a general model in hydrodynamics (ENGLISH)
[ 講演概要 ]
We present a thorough analysis of the Navier-Stokes-Nernst-Planck-Poisson equations. This system describes the dynamics of charged particles dispersed in an incompressible fluid.
In contrast to existing literature and in view of its physical relevance, we also allow for different diffusion coefficients of the charged species.
In addition, the commonly assumed electro-neutrality condition is not required by our approach.
Our aim is to present results on local and global well-posedness as well as exponential stability of equilibria. The results are obtained jointly with Dieter Bothe and Andre Fischer at the Center of Smart Interfaces at TU Darmstadt.

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